Abstract
Profile measurement is a key technical enabler in the manufacturing of highly curved freeform surfaces due to their complex geometrical shape. A current optical probe was used to measure nearly rotary freeform surfaces with the help of one rotation axis, because the probe needs to measure along the normal vector of the surface under the limitation of the numerical aperture (NA). This kind of measuring system generally has a high cost due to the high-precision, multi-axis platform. In this paper, we propose a low-cost, dual-axis rotation scanning method for a highly curved freeform surface with an arbitrary shape. The optical probe can scan the surface profile while always keeping consistent with the normal vector of the measuring points with the help of the double rotation axis. This method can adapt to the changes in curvature in any direction for a highly curved freeform surface. In addition, the proposed method provides a system error calibration technique for the rotation axis errors. This technique can be used to avoid the dependence of the measuring system on the high-precision platform. The three key system errors that affect the measurement accuracy such as installation error of the B-axis, A-axis, and XZ perpendicularity error are first analyzed through establishing an error model. Then, the real error values are obtained by the optimal calculation in the calibration process. Finally, the feasibility of the measurement method is verified by measuring one cone mirror and an F-theta mirror and comparing the results to those obtained using commercial equipment. The maximum measurable angle of the system is ±90°, the maximum measurable diameter is 100 mm, and the measurement accuracy of the system reaches the micron level in this paper.
Highlights
Optical freeform surfaces are widely used in space optics, projection optical systems [1–3], medical endoscope systems [4–6], and other fields because of their complex surfaces and multiple degrees of freedom
Due to the complex geometric characteristics of highly curved freeform surfaces, the traditional measurement methods are limited by the measurement range and numerical aperture (NA, the product of the half-angle of the objective’s collection cone and the index of refraction of the immersion medium) [9] of the probe, which cannot precisely measure the full surface topography of a highly curved freeform surface
Conclusions matrix for any point P0 that rotates θ degrees around the rotation axis determined by (a, b, c, l, m, n) is: 5.1
Summary
Optical freeform surfaces are widely used in space optics, projection optical systems [1–3], medical endoscope systems [4–6], and other fields because of their complex surfaces and multiple degrees of freedom. In the error modeling of a measurement system with multiple degrees of freedom, Du proposed a self-calibration technique for a five-axis, laser-optical measurement system based on a ball bar [23]. He used the parameter estimation method to obtain the system model’s parameters through the ball bar. Zhang set up a noncontact scanning measurement system for a four-axis blade profile [24] He established a multi-body mathematical model to calculate the measurement space coordinate transformation matrix and used a threebeam interferometer and a standard gauge block to verify the geometric error of the system. The feasibility of the proposed measurement method is verified by measuring typical devices and comparing the results with those obtained using advanced commercial equipment
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